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The Dow closed down 287 points, erasing all of its gains for the year. The S&P 500 lost 0.4 percent, with materials, industrials and tech all falling. The Nasdaq shed nearly 0.3 percent.

"At some point you've got to wonder how many times stocks are going to react to the same general bit of news. It may all just be a game of one-up-manship as a negotiating tactic to get to some sort of deal," said Willie Delwiche, investment strategist at Baird. However, "with investor optimism as high as it is, there might not be much margin for error, and there is a real risk that this starts to erode consumer and business confidence."

Shares of some of the biggest chipmakers fell given their large exposure to China. Qualcomm and Nvidia both dropped at least 1.5 percent. On average, semiconductor and semiconductor equipment companies get 52 percent of their revenue from China, according to a recent report from Morgan Stanley.

Ford Motor, which also does a large amount of business in China, saw its stock pull back about 2.2 percent. Meanwhile, Caterpillar and Boeing — considered to be two bellwethers for trade tensions on Wall Street —both dropped at least 3.5 percent.

Trump asked the United States Trade Representative to identify $200 billion worth of Chinese goods for additional tariffs, at a rate of 10 percent. If China "refuses to change its practices" and insists on continuing with the new tariffs it recently declared, then the additional levies would be imposed on Beijing, Trump said Monday night.

Soon after, the Chinese Commerce Ministry issued a response, stating that the latest threat of more tariffs violates previous negotiations and consensus reached between both the U.S. and China. "The United States has initiated a trade war that violates market laws and is not in accordance with current global development trends," the ministry said.

Further tension in U.S.-China relations could end up hurting some iconic U.S. companies the most, said Jim O'Neill, an economist and the chairman of think tank Chatham House.

"I often say to people that America's most iconic modern company, Apple, has for three years sold more iPhones to Greater China than it has to the U.S. So ultimately, if the U.S. genuinely takes this kind of belligerent stance, it's going to be the U.S.' best-growing companies that will suffer," O'Neill told CNBC.

Treasury prices rose on Tuesday, with investors looking for safety amid the stock-market sell-off. The benchmark 10-year note yield dropped to 2.873 percent from about 2.91 percent on Monday.

Commodities, meanwhile, fell sharply as soybeans futures reached their lowest prices in more than two years.

Lindsey Piegza, chief economist at Stifel, said in a note that "we estimate tariffs on goods both ways would likely shave off a few tenths of a percentage point off each country's GDP. While a seemingly minimal impact, as the domestic economy continues to struggle to maintain a near 2% growth rate, a loss of even a few tenths is an unwelcome impact.

"Additionally, the fear from here is a continued back and forth, escalating trade penalties on both sides with a further negative impact on growth," she said.